Spacetime equalization in a wireless receiver

ABSTRACT

A wireless receiver receives signals at a plurality of antennas and the combined signal is compensated for channel distortion. In other aspects, a wireless receiver includes a minimum distance receiver applied to the output of a whitened-matched filter, which combines channel matched filtering and whitening, using one or more antennas.

BACKGROUND OF THE INVENTION

Wireless networks have become increasingly popular, as computers andother devices can be coupled for data communications without requiringwired connections between the network nodes. One set of standards forwireless networks is the IEEE 802.11 standards, but other wirelessstandards or protocols might be used instead. Because wireless networksare expected to operate in unfavorable conditions, such as in thepresence of reflections, interference, movement ofreceivers/transmitters, etc., much effort is needed to correctlytransmit and receive data over a wireless channel.

A typical node in a wireless network (referred to in the standards as a“station”) includes a receive chain and a transmit chain. A transmitchain typically includes some digital processing and analog, RFcircuitry that causes a signal to be transmitted into the wirelesschannel. A receive chain typically includes one or more antenna, RF andanalog circuitry, and digital processing that seeks to output a datastream that represents what the sending transmit chain received as itsinput and transmitted into the wireless network. In some cases, areceiver uses multiple antennas to improve reception of the signal froma sending transmit chain.

Because of the expected conditions, the receive chain includes variouscomponents designed to ensure that signals can be largely recoveredcorrectly. Several techniques have been in use to recover signals.

One technique is the use of a minimum distance receiver (MDR). An MDRuses an estimate of the channel response and knowledge of all of thepossible transmitted signals.

The MDR compares a received signal with each of the possible transmittedsignals (after the channel response is applied to those possibletransmitted signals). Some MDRs might not examine each possibletransmitted signal, if they have a mechanism for ignoring clearlyunlikely ones of the possible transmitted signals, but generally thecomplexity of the search relates to the number of possible transmittedsignals. A minimum distance receiver gets its name from the idea that a“distance”, such as a Euclidean distance, can be calculated between thereceived signal and a possible transmitted signal adjusted by thechannel response. The possible transmitted signal (or signals) thatresult in the minimum distance is judged to be what was sent. It hasbeen shown that a minimum distance receiver (“MDR”) achieves the lowesterror probability in the presence of Gaussian noise, which is a widelyaccepted noise model.

In normal operation of a wireless system, multiple symbols aretransmitted through a wireless channel successively. Channel distortioncauses the time extent of the symbol to increase, so that energy fromone symbol spills into the time window for another symbol, smearing thesymbols together. This effect is referred to as inter-symbolinterference (“ISI”).

In the case in which one isolated symbol is transmitted (so that no ISIis will occur), the MDR selects as the presumed transmitted symbol thesymbol that satisfies Equation 1, where r is the received signal, C isthe channel response and {S_(k)} is the set of possible transmittedsymbols.

$\begin{matrix}{{{{\min\limits_{k}}r} - {Cs}_{k}}}^{2} & \left( {{Equ}.\mspace{14mu} 1} \right)\end{matrix}$

Of course, symbols are typically not transmitted in isolation. Ingeneral, multiple symbols are transmitted in succession, which isreferred to herein as a “sequence”. A typical sequence in a wirelesssystem might be a complete set of symbols that make up a packetaccording to protocols used in the wireless channel, but a sequence neednot be an entire packet or a single packet. With multiple symbols,inter-symbol interference can be expected. However, the sequenceboundaries are typically such that an MDR can assume that there is nointer-sequence interference and the MDR can operate on the sequence.

Thus, where ISI is present, the MDR operates over a sequence rather thanbeing able to deal with single symbols ignoring all other symbols. Thismeans that it might not be sufficient to treat each symbol in isolation,but instead the MDR needs to determine what sequence was sent among allpossible sequences. To do so, the MDR finds the sequence of symbols thatsatisfies a similar condition as in the case where only a single symbolis relevant. An example of such a condition is shown in Equation 2, inwhich r is the received signal, h is the channel response and {p_(k)} isthe set of all possible sequences.

$\begin{matrix}{\min\limits_{p_{k}}{{r - {h*p_{k}}}}^{2}} & \left( {{Equ}.\mspace{14mu} 2} \right)\end{matrix}$

As illustrated by Equation 2, the complexity of the MDR can be expectedto grow exponentially with the length of the sequence. Even efficientapproaches for implementing the MDR, such as using a Viterbi algorithm,may prove to be too complex to implement, given likely receiverconstraints on time, computing power, and power consumption.

In many modulation schemes, the input data is mapped to symbols thatcomprise multiple signal samples. Examples of this are block codes, inparticular, complimentary code keying (“CCK”) codes and Barker codes.For example, a CCK symbol comprises eight quadrature phase shift keying(“QPSK”) encoded “chips”. The channel distortion might smear theboundaries between chips within a symbol. This latter effect is referredto as inter-chip interference (“ICI”).

An MDR can operate on a symbol to compensate for ICI, but selecting thesymbol among the possible transmitted symbols that minimizes thedistance between a group of received samples (e.g., chips) taking intoaccount the estimated channel response due to that symbol. Such an MDRis referred to herein as a Symbol-by-Symbol Minimum Distance Receiver(SbS MDR). For many sequences of symbols, an SbS MDR is easier toimplement than an MDR that compares over all possible sequences, howeverwhile an SbS MDR compensates for smearing within a symbol, it ignoresinterference between symbols (ISI).

Another technique for IS compensation is the decision feedback equalizer(“DFE”). With a DFE, the determination of a current symbol beingdetected takes into account the results of detecting previous symbols.In effect, once it is assumed what the previous symbols were, assumedinterference is calculated for those previously detected symbols and issubtracted from the received signal representing the current symbolprior to a symbol decision on the current symbol. Once that interferencecontribution is subtracted, the remainder is used as the basis for aminimum distance calculation, symbol by symbol.

The energy from interfering symbols that have not yet been determinedwhen a decision is being made on a current symbol is referred to aspre-cursor ISI energy (those undetermined symbols are “behind” thecursor “pointing” to the current symbol being determined). Since a DFErelies on the determination of the previous symbols, it can do well inremoving from a current symbol the ISI from those previous symbols, butcannot do well in removing the energy from pre-cursor symbols, as thosesymbols are not yet known.

Thus, if most of the ISI is from previous symbols, then the DFE removesmost of the ISI. Whether the ISI is primarily from the previous symbolsdepends on which samples are used to make a symbol decision. For finiteextent channels, there are always samples that contain little ISI from agiven symbol. In general, these samples may also contain little energyfrom the current symbol, so this presents a trade-off in that the set ofsignal samples that minimizes ISI from subsequent symbols might not bethe most optimal set of signal samples in terms of signal-to-noise ratio(“SNR”) for the current symbol determination. This might be due to theset of signal samples having only a small amount of energy contributedfor the current symbol.

A DFE works best when the pre-cursor ISI energy is lower. One approachto dealing with ISI is to use an SbS MDR and a DFE applied to the outputof a channel matched filter. This combination gives rise to asignificant reduction in complexity relative to an MDR that operatessequence-by-sequence, however, it is often the case that this does notprovide the highest SNR for the current symbol and lowest amount ofpre-cursor ISI energy.

Additional improvements might be needed under adverse conditions.

BRIEF SUMMARY OF THE INVENTION

In one embodiment of a wireless receiver according to the presentinvention, signals are received at a plurality of antennas and thecombined signal is compensated for channel distortion. In other aspectsof embodiment of a wireless receiver according to the present invention,the wireless receiver includes a minimum distance receiver applied tothe output of a whitened-matched filter, which combines channel matchedfiltering and whitening, using one or more antennas.

A further understanding of the nature and the advantages of theinventions disclosed herein may be realized by reference to theremaining portions of the specification and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a simple wireless network that might usethe present invention.

FIG. 2 is a block diagram illustrating the coupling between one basicservice station and one access point station of the wireless networkshown in FIG. 1.

FIG. 3 is a generalized block diagram of a receive section of stationhardware as might be used in hardware illustrated in FIG. 2 withimprovements according to embodiments of the present invention; FIG. 3Aillustrates a single antenna receiver and FIG. 3B illustrates a multipleantenna receiver.

FIG. 4 is a block diagram of a receive section including awhitened-matched filter (WMF) and a symbol-by-symbol minimum distancereceiver (SbS MDR).

FIG. 5 is a block diagram of a receive section including awhitened-matched filter (WMF) and an SbS MDR with multiple antennas.

FIG. 6 is a block diagram of a receive section including awhitened-matched filter (WMF), an SbS MDR and a feedback filter, withmultiple antennas.

FIG. 7 is a block diagram illustrating one combination of a channelmatched filter and a whitening filter.

FIG. 8 is a block diagram illustrating another combination of channelmatched filters, prior to a summer, and a whitening filter following thesummer.

FIG. 9 is a block diagram of one implementation of an SbS MDR.

FIG. 10 is a block diagram of a receive section including a firstcombined filter combining a matched filter and WMF and a second combinedfilter combining the matched filter and a feedback filter.

FIG. 11 is a block diagram of a receive section including a distinctchannel matched filter, a first combined filter combining a matchedfilter and a whitening filter and a second combined filter combining thematched filter and a feedback filter.

FIG. 12 is a block diagram of a multi-antenna receive section includinga mean-square error equalizer, a complimentary code keying (“CCK”)correlator and a slicer.

FIG. 13 is a block diagram of a multi-antenna receive section includinga mean-square error equalizer, a CCK correlator, a slicer and a feedbackfilter.

FIG. 14 is a block diagram of an SbS MDR for a Barker demodulator,including a Barker correlator and a Barker slicer.

FIG. 15 is a block diagram of an SbS MDR for a CCK demodulator,including a CCK correlator and a CCK slicer.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates a simple wireless network that might use the presentinvention. As shown in FIG. 1, a wireless network 10 comprises aplurality of stations 12 wherein each station 12 is capable ofcommunicating with at least one other station 12 of wireless network 10.In specific implementations, wireless network 10 is a local areawireless network, as might be used within a building, campus, vehicle orsimilar environments. In a specific embodiment, wireless network 10 isdesigned to be compliant with one or more of the IEEE 802.11 standards.However, it should be understood that other standards and nonstandardnetworks might be substituted therefore to solve problems similar tothose solved in the 802.11 environment.

As shown, some of the stations are coupled to client devices 14, whileother stations are coupled to access points 16 that interface todistribution systems such as wired local area network (LAN) connections.For example, station 12(1) is coupled to client device 14(1), whilestation 12(3) is coupled to an access point 16. FIG. 1 is intended to bea simplified and generalized diagram of a wireless network. Interferingsignal generators are not shown, but are assumed to be present.

Examples of client devices 14 include laptops, personal digitalassistants (PDAs), or any other portable or semi-portable electronicdevice needing to communicate with other devices, or a stationaryelectronic device needing to communicate with other devices where a wireconnection to a network or the other devices is not available or easilyprovided. Access points 16 couple their respective stations to adistribution system. Examples of such distribution systems include theInternet, a local area network (LAN) or a public or private connectionto a TCP/IP packet network or other packet network or networks.

In a typical operation, a plurality of station devices are outfittedwith circuitry and/or software that implements a station 12functionality and one or more network access points are provided inwireless network 10 to provide access between such a station device andthe network to which a wired network interface is coupled. A stationcoupled to a wired network interface is referred to as an “accesspoint”. Just one example of the uses of such a system is to connectcomputers within a building to a network without requiring network wiresto be run to each computer. In that example, the building would beoutfitted with stationary access points coupled to the network which arewithin wireless communication range of wireless network cards in each ofthe stations coupled to the network.

FIG. 2 shows in more detail the coupling between one device and onenetwork connection. As shown there, client device 14 is coupled to adevice I/O section of client station hardware 20. Client stationhardware 20 includes a transmit section and a receive section, eachcoupled to the device I/O section. The transmit section transmits asignal through a wireless channel 21 to a receive section of accesspoint hardware 22. That receive section is coupled to a network I/Osection, thus providing a data communication path from client device 14to a distribution system 28 such as a local area network. A path fromdistribution system 28 to client device 14 is also provided, via thenetwork I/O section of access point hardware 22, a transmit section ofaccess point hardware 22, a receive section of client station hardware20 and the device I/O section of client station hardware 20. Thecharacteristics of wireless channel 21 depend on many factors, such asthe location of client station hardware 20 and access point hardware 22as well as intervening objects, such as walls, buildings and naturalobstructions, as well as influences by other devices and transmittersand receivers and signal-reflecting surfaces. The stations can beimplemented by dedicated hardware, a general purpose processor runningstation code, or a combination thereof.

Typically, client station hardware 20 can be integrated in with clientdevice 14. For example, where client device 14 is a laptop computer,client station hardware 20 might be an add-on PCMCIA card that isinserted into the laptop's PCMCIA slot. Typically access point hardware22 is implemented as part of a wired network interface device that isjust used to couple a wired network to a wireless network.Notwithstanding the typical implementation, it should be understood thatnothing here prevents the diagram of FIG. 2 from being entirelysymmetrical, i.e., wherein client station hardware 20 and access pointhardware 22 are nearly identical instances of hardware devices, howeverin many cases, an access point will be fixed and the station that is notan access point is a portable or mobile device where power usage, cost,weight and/or size are considerations.

What follows is a detailed description of a receive section. FIG. 3illustrates components of a receive section. FIG. 3A illustrates areceiver 30 with a single receive antenna, while FIG. 3B illustrates areceiver 40 with multiple receive antennas.

Receiver 30 is shown comprising an RF section 32 that receives a signalfrom an antenna and provides a baseband digital signal 36 to a digitalsignal processing (“DSP”) section 34, which outputs (data output 38) thereceiver's best estimate of the transmitted data that resulted in thereceived signal. In other variations, the baseband signal is digitizedat an input of DSP section 34.

Receiver 40 is shown comprising a plurality of RF sections 42 thatreceive signals from their respective antennas and provide a basebandsignal to single antenna processing sections 44, which then providetheir output, typically in digital form, to a multi-antenna processingsection 46 that combines the information over multiple antennas to forma data output 48, which is the receiver's best estimate of thetransmitted data that resulted in the received signal. Section 46 mightinclude digital signal processing instructions for implementingcomplimentary code keying (“CCK”) and/or Barker demodulation processes.If implemented by digital signal processing, single antenna processingsections 44 and multi-antenna processing section 46 might be implementedby code running on one processor, but where plural processing units orprocessors are available, some parallel processing might occur. Forexample, one or more section 44, but less than all, might run on oneprocessor while other processors handle the other sections.

Further details of elements of receivers not more fully described hereinare shown in U.S. patent application Publication No. US 2002/0094041 A1for Kopmeiners et al. (hereinafter “Kopmeiners”) and U.S. Pat. No.______[U.S. patent application Ser. No. 10/068,360, filed on Feb. 5, 2002 andentitled “Multi-Antenna Wireless Receiver Chain with Vector Decoding”],which are incorporated by reference herein for all purposes. It shouldbe understood that the present invention is not limited to theparticular receiver implementations shown here or there.

Throughout this disclosure, where there are multiple instances of anobject and the number of instances is not critical, the instances arenumbered from “1” to “n” with the understanding that the value of“n”need not be identical from use to use. For example, “n” is used as thenumber of antennas in various places, but that number might vary fromexample to example. It should also be understood that nothing hererequires that all instances be used. For example, the receiverillustrated in FIG. 3B might be designed with ten antennas, but onlyseven of which are being used. This may be for power-saving purposes,because they are not needed when a signal is sufficiently clear, orbecause the signal levels on the unused antennas are too low to providea contribution to the detecting process. Thus, “n” might take ondifferent values in different contexts—in the above example, n=10 if allantennas are counted, whereas n=7 if only active antennas are counted.Generally, n>1 for multi-antenna receivers, but it is possible thatunder some conditions, n=1 (i.e., only one of the n antennas is active),albeit with the attendant loss in information. The number of antennascan be from one to twenty, or more than twenty.

It should be understood throughout this disclosure that the lines shownin the figures could be digital signal lines for communicating a timesequence of complex-valued quantities. It should be further understoodthat operator objects such as summers might be complex summers. In othercases, the signals communicated might be analog signals, control signalsor streams of one or more values.

Overview of Receiver Implementations with Spacetime Equalization

The following disclosure describes the use of multiple receive antennasfor mitigating the distortion caused by the frequency selectivity of thewireless channel, but aspects of what is described might be used as wellwith single receive antenna receivers. In a number of examples, thesignals are modulated using Barker and CCK modulation, as these arecommon and widespread modulations used in wireless systems today,however it should be understood that the teachings of this disclosureare applicable to other existing, and later developed, modulationschemes, unless indicated otherwise.

Using multiple receive antennas for a Barker/CCK receiver withappropriate signal processing can provide increased resistance tofrequency-selective channel distortion as compared to single receiveantenna systems. A simple example of this is the reduction in effectivedelay spread that occurs when the receive antennas are processed with abank of channel matched filters and the results combined. The combinedchannel/channel matched filter responses combine coherently for the peakcorrelation value and destructively away from the peak. In the combiningprocess, the channel side lobes are reduced and the channel iseffectively shorter. This simple scheme can be used to enhance theperformance of single antenna signal processing schemes by acting as afront-end that reduces the delay spread into the rest of the receiver.

In an improved receiver according to embodiments of the presentinvention, a whitened-matched filter is provided in a receiver chainprior to an SbS MDR, as illustrated in FIG. 4. As shown there, a signalmight be received by an antenna 60 and provided to a whitened-matchedfilter (“WMF”) 62, possibly via an RF circuit and/or analog-to-digital(A/D) converter, not shown. The output of WMF 62 is provided to an SbSMDR 64, which then outputs the received data. Examples of MDRs that canbe modified as described herein are the MDR and variations shown inKopmeiners.

As SbS MDR 64 operates over symbols, it determines a minimum distancecomputed over a single symbol, such as a collection of CCK chips thatcomprise one CCK symbol. It should be noted that, when used as taughtherein, the SbS MDR is much more efficient in an implementation than anMDR that operates over a packet or sequence of symbols. In the absenceof ISI, the performance would be the same between the SbS MDR and thefull MDR, but typically a packet will comprise multiple symbols in quicksuccession.

By using the WMF, pre-cursor ISI is compensated for, the DFE compensatesfor post-cursor ISI and the SbS MDR deals with ICI (over the CCK chips,Barker Chips, or the like), as the SbS MDR is applied to the receivedsamples on a symbol-by-symbol basis after the ISI is removed resultingin the benefits of a full MDR, but with much less complexity. Thus, theWMF/DFE combination compensates for the ISI so the input to the SbS MDRshould be free of ISI, but may contain ICI. The SbS MDR takes intoaccount the ICI when making symbol decisions.

The coding used can be either Barker coding or CCK coding for 802.11signaling, or other coding depending on the signaling protocols used.However, in typical cases, Barker coding is robust enough, relative toCCK coding, that multiple antennas, an SbS MDR and a WMF might not beneeded to achieve sufficient performance.

FIG. 5 illustrates a similar improved receiver, having multipleantennas. As shown there, a plurality of signals might be received byantennas 70(1) . . . 70(n) and provided to a whitened-matched filter(“WMF”) 72 that combines contributions from the plurality of antennas.The output of WMF 72 is provided to an SbS MDR 74, which then outputsthe received data. The output of WMF 72 could be one signal, or onesignal per active antenna, or one signal per antenna. An exampleimplementation of WMF 72 with a single signal output is illustrated inFIG. 8, wherein channel matched filters are applied, the channelscombined and then a whitening filter applied, where the whitening filteris built using the combined channel response.

FIG. 6 illustrates an improved receiver having multiple antennas similarto that of FIG. 5, further including feedback. In that receiver, aplurality of signals might be received by antennas 80(1) . . . 80(n) andprovided to a whitened-matched filter (“WMF”) 81 that combinescontributions from the plurality of antennas. The receiver also includesan SbS MDR 82 and a feedback filter 83. The output of feedback filter 83is combined with the output of WMF 81 by a summer 84. The output ofsummer 84 forms an input to SbS MDR 82 and SbS MDR 82 provides signalsat its one or more output that form the detected data stream and aninput to feedback filter 83. Feedback filter 83 together with a decisionblock, such as a slicer (not shown), in SbS MDR 82 effects a decisionfeedback equalizer (“DFE”).

It should be noted that while a summer 84 is shown as a distinct block,other methods of combining the outputs might be used instead. In aparticular embodiment, summer 84 is a complex adder that adds thesignals. Of course, in a common implementation, many of the functionalblocks are implemented by digital signal processing code and/orhardwired logic. In such implementations, summer 84 might by fullyimplemented by a single “add” instruction.

FIG. 7 is a more detailed block diagram of one implementation ofwhitened-matched filter (“WMF”) 72 shown in FIG. 5, for a single antennareceiver. WMF 72 combines a channel matched filter (“CMF”) 76 and awhitening filter (“WF”) 78. In embodiments where filters are implementedas instructions for hardwired logic or digital signal processor code,the functions of CMF 76 and WF 78 might be integrated such that they arenot distinct objects. CMF 76 might be implemented as H*(1/z*) where H(z)is the z-transform of the channel. WF 78 might be implemented to performthe filtering function shown in Equation 4, below.

FIG. 8 is a more detailed block diagram as a counterpart to FIG. 7, butwherein multiple antennas are considered. There, WMF 81 comprises aplurality of channel matched filters 86, whose outputs are combined by asummer 87 that provides its sum output as an input to a whitening filter(“WF”) 88. WF 88 might be identical to WF 78, but it might also bedifferent. For example, in the preferred embodiment, WF 88 is designedto be the reciprocal maximum-phase spectral factor of the combinedchannel response. In embodiments where filters are implemented asinstructions for hardwired logic or digital signal processor code, thefunctions of filters 86, summer 87 and filter 88 might be integratedsuch that they are not distinct objects.

By applying the feedback to the output of the WMF instead of to theoutput of the channel, detection is improved. The output of the WMF is asignal that is “minimum-phase”, which is a property that ensures thatsamples used in detecting a symbol that maximize SNR have smearingsolely from previous symbols, i.e., little or no pre-cursor energy.

An SbS MDR and a DFE applied to the output of a channel matched filterdoes not provide the highest SNR and lowest amount of pre-cursor ISIenergy (i.e., the energy of ISI contributed by samples transmitted afterthe sample under consideration). A combination of an SbS MDR with adecision feedback equalizer applied to the output of a whitened-matchedfilter provides an optimal trade-off between maximizing SNR andminimizing pre-cursor distortion. The “minimum-phase” property of theoutput of the WMF is a property that squarely addresses the trade-offdescribed above. This might be illustrated by the following equations.

Where H(z) represents the z-transform of the channel, under a mildcondition such as the Paley-Wiener criteria, the spectrum of the channelcan be factored as shown in Equation 3, such that the component G(z) hasall of its poles and zeros inside the unit circle.S _(H)(z)=A _(H) ² G(z)G*(1/z*)  (Equ. 3)

A linear system whose poles and zeros are all inside the unit circle is“minimum-phase”. By applying a channel matched filter to the receivesignal, the combined response of the channel and channel matched filterwill have z-transform given by S_(H)(Z) in Equation 3. By then applyinga filter with z-transform shown in Equation 4 to the output of thematched filter, the resulting signal will be minimum-phase.

$\begin{matrix}\frac{1}{A_{H}^{2}G*\left( {1/z^{*}} \right)} & \left( {{Equ}.\mspace{14mu} 4} \right)\end{matrix}$

The DFE benefits from a minimum-phase signal, as that signal hasdesirable properties. For example, some samples are used in detecting asymbol and the selection of samples that maximizes the SNR is aselection of samples for which it is expected that any smearing thatoccurs will be solely from previous symbols, which the DFE attempts tocancel out. Applying a whitened-matched filter and a DFE at the symbollevel instead of the chip level improves performance.

A filter with the z-transform shown in Equation 4 is referred to as awhitening filter. Herein, the combined response of a channel matchedfilter and a whitening filter is referred to as the whitened-matchedfilter.

Variations of Implementations

Basic Implementation

In a basic implementation of a DFE and WMF described below, both thewhitened-matched filter and data decisions are applied to individualchips. For Barker modulated signals and CCK modulated signals, datadecisions can be made on groups of chips (i.e., symbols) and there arebenefits to considering a group of chips as a whole rather than tryingto decide on each chip in isolation.

Consider CCK modulation, for example. A CCK symbol comprises eightchips. If a receiver made hard decisions at the chip level, it wouldlose the processing gain that comes from the CCK modulation. In order tokeep this gain, typically a full eight chips from a symbol need to beprocessed prior to detection. Consider the output of thewhitened-matched filter. With an output collected into sets of 8samples, the result is a large number of possible symbols for the SbSMDR to select from.

The SbS MDR attempts to minimize a distance value, D, for eachcollection, r _(k), of receive samples according to an equation such asEquation 5, wherein s _(l) represents one of the possible transmitsymbols, G_(k) represents matrices with rows corresponding to theimpulse response of the minimum-phase spectral factor of the channel andthe sum is over all possible transmit symbols.

$\begin{matrix}{D = {{{\underset{\_}{r}}_{k} - {\sum\limits_{l \leq k}{G_{k - l}{\underset{\_}{s}}_{l}}}}}^{2}} & \left( {{Equ}.\mspace{14mu} 5} \right)\end{matrix}$

The computational effort can be reduced by assuming that at any ISIpresent at the output of the whitened-matched filter is contributed onlyfrom the previous symbol. Equation 5 can be then written as shown inEquation 6.D=∥r _(k) −G ₁ s _(k−1) −G ₀ s _(k) ∥²  (Equ. 6)

With a DFE in place, interference from the previous symbol, G₁ s _(k−1),is removed, leaving the simplified Equation 7.D=∥r _(k) −G ₀ s _(k) ∥²  (Equ. 7)

Equation 7 is one mathematical representation of an SbS MDR. MinimizingD from Equation 7 is equivalent to finding the symbol s that maximizes Min Equation 8, where s^(T) and G₀ ^(T) are the conjugate transposes of sand G₀, respectively.

$\begin{matrix}{M = {{{Re}\left\{ {{\underset{\_}{s}}^{T}G_{0}^{T}{\underset{\_}{r}}_{k}} \right\}} - {\frac{1}{2}{{G_{0}\underset{\_}{s}}}^{2}}}} & \left( {{Equ}.\mspace{14mu} 8} \right)\end{matrix}$

This can be implemented as an additional matched filter and CCKcorrelator with corrections applied to the correlator output prior toslicing. An example of such an implementation of an SbS MDR is shown inFIG. 9.

FIG. 9 shows one example of an SbS MDR 90 (as SbS MDR 82 in FIG. 6, forexample) in greater detail, including an SbS MDR matched filter (“SMMF”)92 and a core 91 comprising a correlator 94, a summer 95, correctionweights 96 and a slicer 98. SMMF 92 matches SbS MDR 90 to the combinedresponse of the channel and the WMF (not shown here; example: WMF 81 inFIG. 6).

An input to SbS MDR 90 from a summer (not shown), such as summer 84 ofFIG. 6, is provided to SMMF 92, the output of which is provided tocorrelator 94. An output of correlator 94 is summed with correctionweights 96 by summer 95, which provides its result to slicer 98. Thus,corrections are applied to the output of correlator 94 prior to slicing.The correction weights correspond to energy in a symbol at the outputoff the channel, which are preferably subtracted from the correlatoroutput prior to slicing. One implementation for determining suitablecorrection weights in described below, including one example inEquations 21–22.

Correlator 94 can be a CCK correlator or a Barker correlator or othercorrelator, depending on the code being used. SMMF 92 can be combinedwith the WMF and feedback filter to reduce the overall complexity of theimplementation. An example of this is shown in FIG. 10.

As shown in FIG. 10, a filter 100 is a combination of a WMF and the SMMFand the SMMF is also combined with the feedback filter to form acombined filter 104. In one implementation, filter 100 is a combinationof SMMF 92, shown in FIG. 9 and described above, with WMF 81 describedabove in connection with FIG. 7. In one implementation, filter 104 is acombination of SMMF 92 with feedback filter 83 described above inconnection with FIG. 6.

The combination of the SbS MDR matched filter and whitening filter isinteresting conceptually as well as in terms of implementation. Thematrix G₀ ^(T) represents truncated versions of the maximum-phasespectral factor of the channel. The transfer function of the whiteningfilter is the reciprocal of the maximum-phase spectral factor of thechannel, so application of G₀ ^(T) to the output of the whitening filtergives rise to cancellation in the combined response. The cancellation iscyclo-stationary with regards to the chips in the symbol. That is, thecombined response for the first chip in a symbol will be nearly theidentity. The combined response for the last chip in a symbol will bethe nearly that of the whitening filter. This generates an effectwherein the whitening filter is removing ISI, but not ICI.

This approach does require more processing for chips later in a symbolthan for the earlier chips. However, since the DFE requires moreprocessing for chips early in the symbol and less for chips later in thesymbol, the total amount of processing can be shared for overall evenloading. FIG. 11 illustrates an allocation of filter function that takesadvantage of this.

As shown in FIG. 11, a CMF 110 receives inputs from antennas andprovides results to a combined filter 112 that combines a matched filter(such as SMMF 92 of FIG. 9) and a whitening filter (such as WF 78 inFIG. 7). The results of the combined filter 112 are added to a feedbackfilter 104 output as described earlier. The feedback filter 104 includesthe matched filter as well.

If CMF 110 is implemented such that it is shorter than the channel, theSMMF that is part of combined filter 112 will not comprise themaximum-phase spectral factor of the channel. If CMF 110 is not soimplemented, it can still work, but computation of the filtercoefficients is a more complex operation.

EXAMPLE

An example implementation will now be described, with reference tovarious figures, for a given channel. From this example, filtercoefficients for feedforward and feedback matched filters (elements 112and 104 in FIG. 11) for a minimum distance DFE receiver are determinedfrom a given channel characteristic. Consider a channel with z-transformshown in Equation 9. The channel matched filter is for that channelwould be as shown in Equation 10.H(z)=1+0.5z ⁻¹  (Equ. 9)H*(1/z*)=0.5z+1=z(0.5+z ⁻¹)  (Equ. 10)

To compute the whitening filter, a Levinson recursion might be used, butother approaches can be used. The autocorrelation of the channelresponse is as shown in Equation 11. A Levinson recursion solves thesystem shown in Equation 12 for the forward prediction-errorcoefficients {a_(i)}.

$\begin{matrix}{{{R(k)} = 1.25},{.5},0,0,\ldots} & \left( {{Equ}.\mspace{14mu} 11} \right) \\{{\begin{pmatrix}{R(0)} & {R(1)} & {R(2)} & \ldots \\{R(1)} & {R(0)} & {R(1)} & \ldots \\{R(2)} & {R(1)} & {R(0)} & \ldots \\\vdots & \vdots & \vdots & ⋰\end{pmatrix}\begin{pmatrix}1 \\a_{1} \\a_{2} \\\vdots\end{pmatrix}} = \begin{pmatrix}\sigma_{e}^{2} \\0 \\0 \\\vdots\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 12} \right)\end{matrix}$

A forward prediction-error filter (an intermediate step in buildingfilters shown in the figures) corresponds to the filter with response:

$\begin{matrix}{\frac{1}{G(z)}.} & \left( {{Equ}.\mspace{14mu} 13} \right)\end{matrix}$

The filter with coefficients given by the conjugate time reversal of theforward predictions-error coefficients has response:

$\begin{matrix}{\frac{1}{G^{*}\left( {1/z^{*}} \right)}.} & \left( {{Equ}.\mspace{14mu} 14} \right)\end{matrix}$

By applying the Levinson recursion to the auto-correlation of thechannel response and taking the conjugate time reversal of thecoefficients, the result is a whitening filter up to a scale factor. Thescale factor A_(H) ² corresponds to the mean-square prediction error andcan be obtained from the Levinson recursion. The Levinson recursionrecursively generates increasingly better approximations to thewhitening filter.

For example, assume the whitening filter is to be a six-tap FIR filter.The first five iterations of the Levinson algorithm give:b ₁(z)=1−0.4z ⁻¹b ₂(z)=1−0.48z ⁻¹+0.19z ⁻²b ₃(z)=1−0.49z ⁻¹+0.24z ⁻²−0.09z ⁻³b ₄(z)=1−0.5z ⁻¹+0.25z ⁻²−0.12z ⁻³+0.05z ⁻⁴b ₅(z)=1−0.5z ⁻¹+0.25z ⁻²−0.12z ⁻³+0.06z ⁻⁴−0.02z ⁻⁵Here, A_(H) ²=1. In this case,w(z)=−0.03+0.06z⁻¹−0.12z⁻²+0.25z⁻³−0.5z⁻⁴+z⁻⁵ would be used as thewhitening filter.

Now consider the feedback filter portion of element 104 in FIG. 11 andthe SMMF. The coefficients of both filters are obtained from themaximum-phase spectral factor of the channel response. The coefficientsof minimum-phase spectral factor {g_(i)} can be obtained from theprediction error coefficients through the relationship shown in Equation15.b(z)g(z)=1  (Equ. 15)Thus,b ₀ g ₀=1

g ₀=1b ₁ g ₀ +b ₀ g ₁=0

g ₁ =−b ₁

g ₁=0.5b ₂ g ₀ +b ₁ g ₁ +b ₀ g ₂=0

g ₂ =−b ₂ −b ₁ g ₁

g ₂=0b ₃ g ₀ +b ₂ g ₁ +b ₁ g ₂ +b ₀ g ₃=0

g ₃ =−b ₃ −b ₂ g ₁ −b ₁ g ₂

g ₃=0 etc.

Not that, in this example, the minimum-phase spectral factor of thechannel auto-correlation is the channel response. The maximum-phasespectral factor is obtained by conjugating and time reversingcoefficients of the minimum-phase spectral factor.

Matrices, G₀ and G₁, shown in Equations 16, 17, respectively, representthe portions of a convolution matrix with coefficients given by theminimum-phase spectral factor that operate and the current and previoussymbol respectively.

$\begin{matrix}{G_{0} = \begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\{.5} & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {.5} & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {.5} & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {.5} & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {.5} & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {.5} & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {.5} & 1\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 16} \right) \\{G_{1} = \begin{pmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & {.5} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 17} \right)\end{matrix}$

The matrix G₀ ^(T) shown in Equation 18 corresponds to the operations ofthe additional matched filter.

$\begin{matrix}{G_{0}^{T} = \begin{pmatrix}1 & {.5} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & {.5} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & {.5} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {.5} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & {.5} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & {.5} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & {.5} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 18} \right)\end{matrix}$

Now consider an implementation in which the feedback coefficients G₁ andthe additional matched filter have been combined. The combined feedbackfilter is given by G₀ ^(T)G₁, and G₀ ^(T)G₁=G₁ for these sets of values.

The feedback filter operates as follows. When processing the first chipof a symbol, is subtracts off 0.5 the value of the last chip of theprevious symbol. In general, the feedback structure will be morecomplex.

Now consider the combined response of the additional matched filter andwhitening filter. Constructing a convolution matrix, W, with rows givenby the response of the whitening filter results in the matrix shown inEquation 19 and a combined response given by Equation 20.

$\begin{matrix}{W = \begin{pmatrix}1 & {- {.5}} & {.25} & {- {.12}} & {.06} & {- {.03}} & 0 & 0 & 0 & \cdots \\0 & 1 & {- {.5}} & {.25} & {- {.12}} & {.06} & {- {.03}} & 0 & 0 & \cdots \\\vdots & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & \cdots \\0 & 0 & 0 & 0 & 0 & 0 & 1 & {- {.5}} & {.25} & ⋰ \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- {.5}} & ⋰\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 19} \right) \\{{G_{0}^{T}W} = \begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \cdots \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \cdots \\\vdots & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & \cdots \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- {.5}} & {.25}\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 20} \right)\end{matrix}$

The combined additional matched filter and whitening filter operate asfollows. For the first seven chips of a symbol, the output of thematched filter passes through unchanged. For the last chip of thesymbol, use the output of the whitened-matched filter.

The output of the DFE is fed to the CCK correlator. Correction weightsare applied to the output of the correlator prior to the making ofsymbol decisions. These weights correspond to the energy of each symbolat the correlator input. For each symbol s_(k), compute ∥G₀s_(k)∥².Consider the 11 Mbps (megabits per second) CCK symbols={1,1,1,−1,1,1,−1,1}.

$\begin{matrix}{{G_{0}s} = \begin{pmatrix}1 \\1.5 \\1.5 \\{- {.5}} \\{.5} \\1.5 \\{- {.5}} \\{.5}\end{pmatrix}} & \left( {{Equ}.\mspace{14mu} 21} \right)\end{matrix}$∥G ₀ s∥ ²=1+2.25+2.25+0.25+0.25+2.25+0.25+0.25=8.75  (Equ. 22)

A similar weight is computed for each symbol. The corresponding value issubtracted from the correlator output prior to slicing.

FIG. 12 is a block diagram of a multi-antenna receive section includinga plurality of channel matched filters 120, a summer 122, a mean-squareerror (MSE) equalizer 124, a complimentary code keying (“CCK”)correlator 126 and a slicer 128. A similar section might be used forBarker codes.

FIG. 13 is a block diagram of a variation of the multi-antenna receivesection of FIG. 12. Here, a summer 129 is interposed between MSEequalizer 124 and CCK correlator 126 to add in an output of a feedbackfilter 130.

FIG. 14 is a block diagram of an SbS MDR for a Barker demodulator,including a Barker correlator and a Barker slicer. The number ofcorrection weights for the Barker correlator could be four or some othernumber.

FIG. 15 is a block diagram of an SbS MDR for a CCK demodulator,including a CCK correlator and a CCK slicer.

Embodiments of the present invention and some variations have now beendescribed. Several embodiments can be used either with a single receiveantenna or with multiple receive antennas. As mentioned, the use ofmultiple receive antennas for combating distortion due to frequencyselective channels shortens the effective delay spread and reduces ISI.

A combined filter that combines a whitening filter and an additionalmatched into one filter gives rise to an efficient computation of filtercoefficients as well as an efficient implementation of the filteringoperations. In some embodiments, the additional matched filter is atruncated version of the inverse of the whitening filter, for additionalefficiency gains.

By combining these filters into one filter, cancellation takes placesuch that the combined filter compensates for inter-symbol interference(“ISI”) but not inter-chip interference (“ICI”). This cancellation givesrise to an implementation that requires fewer operations. There is arelationship (see Equation 15) between the coefficients of the whiteningfilter and additional matched filter that allows the simple computationof one set of coefficients from the other.

By separating the channel matched filter (“CMF”) from the feed-forwardand feed-back equalization, the over-all complexity of the receiver isreduced. Where multiple antennas are used, the CMF takes in multiplereceive channels and provides a single combined response at one of itsoutputs. The feed-forward and feed-back equalizers equalize the combinedchannel response. This separation of processing requires fewercomputations than if the receiver tries to equalize each receive chainseparately. In addition, the design is more flexible since theequalization/detection portion of the design works the same for anynumber of receive chains.

The above description is illustrative and not restrictive. Manyvariations of the invention will become apparent to those of skill inthe art upon review of this disclosure. The scope of the inventionshould, therefore, be determined not with reference to the abovedescription, but instead should be determined with reference to theappended claims along with their full scope of equivalents.

1. A wireless receiver for receiving data over a wireless channel,comprising: a plurality of antennas having signal diversity such thatwhat is received from the wireless channel not identical at each of theplurality of antennas; digital signal processing logic for processingsignals received by the plurality of antennas, wherein the signals areone or more of Barker modulated signals and complementary code keying(CCK) signals; demodulation logic in the digital signal processing logicthat demodulates a set of signals from two or more of the plurality ofantennas, including one or more of a Barker correlator and a CCKcorrelator corresponding to modulation of the set of signals; anddistortion compensation in the digital signal processing logic thatprocesses at least a portion of the set of signals received comprisingportions from signals from at least two of the plurality of antennas tocompensate for channel distortion.
 2. The wireless receiver of claim 1,wherein the demodulation logic comprises a Barker demodulator comprisinga Barker correlator and a Barker slicer.
 3. The wireless receiver ofclaim 1, wherein the demodulation logic comprises a CGK demodulatorcomprising a CCK correlator and a CCK slicer.
 4. The wireless receiverof claim 1, further comprising a mean square error equalizer.
 5. Thewireless receiver of claim 1, further comprising a decision feedbackequalizer.
 6. The wireless receiver of claim 1, further comprising: awhitened matched filter that receives one or more of the signalsreceived by the plurality of antennas and outputs a number of filteredsignals, wherein the whitened matched filter operates on the one or moreof the signals according to a channel matched filter and a whiteningfilter.
 7. The wireless receiver of claim 6, further comprising: afeedback filter; and a symbol by symbol minimum distance receiver (SbSMDR) that receives the number of filtered signals from the sum of thewhitened matched filter and the feedback filter and outputs a resultingdata stream.
 8. The wireless receiver of claim 7, wherein the SbS MDRcomprises: an SbS MDR matched filter, matched to a response of thewhitened matched filter and the wireless channel; a correlator; and aslicer.
 9. The wireless receiver of claim 8, comprising a combinedfilter implementing the SbS MDR matched filter and the whitening filter.10. The wireless receiver of claim 8, comprising a combined filterimplementing the SbS MDR matched filter and the feedback filter.
 11. Thewireless receiver of claim 8, with corrections prior to slicing.
 12. Thewireless receiver of claim 11, comprising a combined filter implementingthe SbS MDR matched filter and the whitening filter.
 13. The wirelessreceiver of claim 11, comprising a combined filter implementing the SbSMDR matched filter and the feedback filter.
 14. A wireless receiver forreceiving data over a wireless channel from a plurality of antennas,comprising: a whitened matched filter that receives two or more inputsignals received from the plurality of antennas and outputs a number offiltered signals including at least one combined filtered signalrepresenting a whitened matched filtered signal with contribution fromthe two or more input sianals, wherein the whitened matched filteroperates on the two or more input signals according to a channel matchedfilter and a whitening filter; and a symbol by symbol minimum distancereceiver (SbS MDR) that receives the number of filtered signals from thewhitened matched filter and outputs a resulting data stream, wherein theSbS MDR comprises: a) an SbS MIDR matched filter, matched to a responseof the whitened matched filter and the wireless channel; b) acorrelator; and c) a slicer.
 15. The wireless receiver of claim 14,comprising a combined filter implementing the SbS MDR matched filter andthe whitening filter.
 16. The wireless receiver of claim 14, comprisinga combined filter implementing the SbS MDR matched filter and a feedbackfilter.
 17. The wireless receiver of claim 14, corrections prior toslicing.
 18. The wireless receiver of claim 17, comprising a combinedfilter implementing the SbS MDR matched filter and the whitening filter.19. The wireless receiver of claim 17, comprising a combined filterimplementing the SbS MDR matched filter and a feedback filter.
 20. Awireless receiver for receiving data over a wireless channel from aplurality of antennas, comprising: a whitened matched filter thatreceives two or more input sianals received from the plurality ofantennas and outputs a number of filtered signals including at least onecombined filtered signal representing a whitened matched filtered signalwith contribution from the two or more input signals, wherein thewhitened matched filter operates on the two or more input signalsaccording to a channel matched filter and a whitening filter; and asymbol by symbol minimum distance receiver (SbS MDR) that receives thenumber of filtered signals from the whitened matched filter and outputsa resulting data stream, wherein the channel matched filter isimplemented as a filter distinct from the SbS MDR matched filter and thewhitening filter.
 21. A wireless receiver for receiving data over awireless channel, comprising: a channel matched filter; a first combinedfilter coupled with an input to receive an output of the channel matchedfilter, wherein the first combined filter operates according to a symbolby symbol minimum distance receiver (SbS MDR) matched filter and awhitening filter; a correlator, coupled to receive an output of thefirst combined filter added to a feedback signal; a slicer, coupled toreceive an output of the correlator added to one or more weights; asecond combined filter coupled to receive a slicer output, wherein thesecond combined filter outputs the feedback signal and operatesaccording to the SbS MDR matched filter and a feedback filter; and adata output for outputting a resulting data stream from an output of theslicer.
 22. A wireless receiver for receiving data over a wirelesschannel, comprising: a plurality of antennas for receiving a pluralityof signals from the wireless channel; a symbol by symbol minimumdistance receiver (SbS MDR); a first combined filter having a transferfunction that is a combination of a channel matched filter and an SbSMDR matched filter, wherein the channel matched filter is matched to achannel response of the wireless channel and the SbS MDR matched filteris matched to the SbS MDR, the first combined filter coupled to provideone or more filtered outputs to the SbS MDR; and a second combinedfilter that combines a transfer function of the SbS MDR matched filterwith a feedback filter that receives an output of the SbS MDR and feedsback a signal to be combined with the one or more filtered outputs at aninput of the SbS MDR.
 23. The wireless receiver of claim 22, wherein theSbS MDR comprises: a correlator; means for weighting signals prior toslicing; and a slicer that slices weighted signals from the correlator.24. The wireless receiver of claim 22, wherein the first combined filterfurther comprises a whitening filter transfer function.
 25. A wirelessreceiver for receiving data over a wireless channel, comprising: one ormore antennas for receiving one or more signals from the wirelesschannel; a symbol by symbol minimum distance receiver (SbS MDR); a firstcombined filter having a transfer function that is a combination of achannel matched filter, a whitening filter and an SbS MDR matchedfilter, wherein the channel matched filter is matched to a channelresponse of the wireless channel and the SbS MDR matched filter ismatched to the SbS MDR, the first combined filter coupled to provide oneor more filtered outputs to the SbS MDR; and a second combined filterthat combines a transfer function of the SbS MDR matched filter with afeedback filter that receives an output of the SbS MDR and feeds back asignal to be combined with the one or more filtered outputs at an inputto the SbS of MDR.
 26. The wireless receiver of claim 25, wherein theSbS MDR comprises: a correlator; means for weighting signals prior toslicing; and a slicer that slices weighted signals from the correlator.